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Theorem nnssn0s 28327
Description: The positive surreal integers are a subset of the non-negative surreal integers. (Contributed by Scott Fenton, 17-Mar-2025.)
Assertion
Ref Expression
nnssn0s s ⊆ ℕ0s

Proof of Theorem nnssn0s
StepHypRef Expression
1 df-nns 28322 . 2 s = (ℕ0s ∖ { 0s })
2 difss 4135 . 2 (ℕ0s ∖ { 0s }) ⊆ ℕ0s
31, 2eqsstri 4029 1 s ⊆ ℕ0s
Colors of variables: wff setvar class
Syntax hints:  cdif 3947  wss 3950  {csn 4625   0s c0s 27868  0scnn0s 28319  scnns 28320
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-dif 3953  df-ss 3967  df-nns 28322
This theorem is referenced by:  nnssno  28328  nnn0s  28333  nnn0sd  28334  nnsgt0  28343
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